Transparency/Masking : See through an Outer Sphere and see Inner Sphere in true colours
You might be able to accomplish the effect you want using Compositing and Render Layers.

https://www.blender.org/manual/render/post_process/layers.html

Put the red sphere on one layer and the blue sphere on another layer.  Make sure the red layer is transparent ( Can Blender render pngs with the background transparent? )

Some of the compositor nodes you would need have screenshots in Using scenes and render layers to composite an object isolated on white background with shadow .


  use an alpha over node in the compositor to put the red ball OVER the
  blue one. Both will keep their solid appearance.
  - Gez


When it comes time for the spheres to swap orders, you can have a second alpha-over node that puts the blue ball over the red ball.  Then route those two alpha-over nodes into a Mix (under the Add > Color menu) node and animate its Fac to switch from 0 to 1.  This animation can be keyframed, or if you want to get super-fancy you can rig a driver that uses python to compare the radius of the two spheres.

Unfortunately the layers property of an object can not be keyframed.  I do not think there is a way to keyframe the visibility of an object within a single layer.  It is possible to animate the hide_render property (the camera icon on the outliner) that affects its visibility on all layers.  This enables an alternative where you just have 3 layers and one of them is an identical blue sphere that is unrenderable until the keyframe where it has shrunk enough that you want it to appear (you could also get fancy and use drivers).  This technique does not require you to keyframe compositor nodes and slightly simplifies the node tree.  It also works better if you have multiple nested spheres in the scene.

Having two distinct blue sphere objects can illustrate some properties of blenders datablock sharing system.  If you animate the sphere and then create a duplicate for the other layer they will share the same action datablock and will animate the same.  If you duplicate the sphere before you give it any keyframes (so at that time the original has no action), the two spheres will not share the action datablock (although you can later link it in using the Action Editor mode of the Dope Sheet window).